TWR chains sub-period returns together. If a portfolio gains 10% in the first half and loses 5% in the second, the time-weighted return is 1.10 x 0.95 - 1 = 4.5%, regardless of whether a large deposit arrived in between.
This is the right measure for comparing a manager against a benchmark, because the manager usually does not control when money arrives. It is the standard behind gips-standards and most published fund performance figures.
It is the wrong measure for an investor asking what they actually earned. Someone who added $500,000 just before the losing half did far worse than 4.5%, which is what money-weighted-return captures.
Related: money-weighted-return, gips-standards, performance-reporting, cagr, benchmark